Before she died, at the age of 81 in 1944, the Swedish artist Hilma af Klint stipulated that her paintings were not to be shown in public for 20 years after her death. Perhaps she felt that the world was not yet ready for them. In some respects, the world never will be ready for the occult symbolism and spiritualist gibberish that her work was derived from, and from which she gained her inspiration. Although the same peculiar beliefs attend the work of pioneering artists such as Mondrian, Kandinsky and Malevich, they never suggested, as did Af Klint, that their work was guided by an imaginary "leader in the spiritual world". For Af Klint, this was a certain Ananda, who in 1904 told her "she was to execute paintings on the astral plane".

By all accounts, Af Klint was a sober, well-balanced woman. Her art and beliefs, however, were extreme. Regarded as a clairvoyant from childhood, she was a medium and one of Sweden's first followers of the theosophical teachings of Madame Blavatsky, and later of Rudolf Steiner's Anthroposophic movement. Her work - and there are over 1,000 paintings - might have disappeared altogether, as the quirky but incomprehensible products of a minor artist. Certainly its resuscitation has been slow, while its value and place are still in debate.

And yet seeing Af Klint's work for the first time, in the largest gallery of the Camden Arts Centre in London, is something of a revelation. As early as 1906, Af Klint was painting abstracts. Her canvases - some unusually large - are filled with grids and intersecting circles, simplified flower forms, gonad-like shapes, flattened cubes, painted numbers, stray, sometimes invented words, spirals, weird vectors, loop-the-loop lines, pyramids and sunbursts. One scrabbles for precedents and connections with other artists, but the references are all retroactive: it is as if Af Klint anticipated moves Matisse didn't make until 1908. She painted watercolour square monochromes in 1916. She made automatist drawings decades before the surrealists. She seems to prefigure painters such as Alfred Jensen and Arthur Dove, as well as early 1980s neo-expressionism and abstractionists such as Beatriz Milhazes and Elizabeth Murray.

But none of this counts for much. What Af Klint appears to share with other artists, either formally or intellectually, also cleaves them apart. There is no irony whatsoever in Af Klint's painting, no consistency and no self-reflection about where any of these strangely prescient leaps might have taken her art. She worked largely, if not entirely, in ignorance and isolation from the ferment of the European avant-garde, and almost solely at the service of her occult beliefs.

Mondrian wrote in 1909: "My work remains entirely outside the occult realm, although I try to attain occult knowledge for myself in order to gain a better understanding of things." Much more recently, the Swiss artist Thomas Hirschhorn said something similar, writing: "I don't need philosophy for my work as an artist. I need philosophy to live." Af Klint was driven in a way that is difficult to deal with. Her art just kept on coming, in all its variety and strangeness, until she died, in the same year as Mondrian and Kandinsky. What for the two men was a generalised utopian spirit, for Af Klint was a matter of personal psychic survival. She must have been incredibly tough.

What is slightly unnerving is that, in 1932, Af Klint produced a number of watercolours predicting the second world war. One, titled A Map/The Blitz, shows a fiery wind, coming from Europe, curling from Southampton round the coast to Liverpool and London. Another map depicts "the fights in the Mediterranean", with a brown cloud spreading over North Africa, southern Italy, Gibraltar and Bordeaux. However, we should be wary of making too much of Af Klint's predictions, or of her status as a revolutionary artist.

In many ways, even her most abstract paintings are diagrams and abstractions from ideas - not wholly abstract, more representations of elements of an unseen world, and of invisible forces. Her art also moved backwards and forwards between the apparently abstract and the embarrassingly kitsch. She was unable to paint convincing figures, astral or otherwise. Simpering nudes and crying nuns were more her line. That said, what arresting images these are. Too often for it to be an accident, Af Klint had an innate sense of how to make a painting, often with no artistic models to turn to. Her best paintings are airy, their forms and geometries delivered with an evident pleasure and openness. She had a great touch, as careless and confident as it was committed. The scale and frontality and freshness of her work still stand up, in a way that many Kandinskys don't. Yet looking at photographic portraits of the artist, we see a stern woman who was far from cosmopolitan, and in whom there are few outward signs of emancipation. For a woman to be an artist at all in Sweden in the early 20th century was difficult enough. To be an artist who believed as she did must have made matters even more difficult.

We might see Af Klint's art and her whole life struggle as symptomatic of an age, a culture and the peculiarities of her psychological and emotional make up. A century ago, the occult, spiritualism and in particular the theosophical teachings of Madame Blavatsky were all the rage. In Paths to the Absolute, his book on the origins of abstraction, John Golding called theosophy "a world of vast, intangible and amorphous ideas". Talking to artists often leads one to such a place, however hard-bitten and sceptical they are, and whatever mental landscape they inhabit. Artists need a strong belief system of some kind, if not to actually underwrite and justify their art, then to gear up their thinking and to influence the kinds of things they might say and do.

What a strange artist Af Klint was. She is being shown at Camden alongside work by a modern German artist, Isa Genzken: they appear to inhabit entirely different, parallel universes.

The best things in Genzken's show are a series of model beach huts, dated 2000, each one standing on its own plinth. Constructed from offcuts of clear plastic, roughly folded aluminium sheet, odd bits of card, small mirrors and all manner of little bricollaged detritus, and set in little beach landscapes of twigs and shells, they are small habitations that recall both their real equivalents and havens of erotic desire. Such places are sexy, as Picasso's 1930s paintings often remind us. But we don't need this memory to be reminded: one of Genzken's huts is wallpapered with porno images of two young men doing something unmentionable. These ramshackle habitations are also bunkers and shanties, wrecked hulks on the edge of the map. Genzken's show is called Sport, and also includes a series of paintings whose sole repeated image is the dangling rings of the aerial gymnast. One thinks of the gymnast's disciplined turns and flight, and of the dangling of a noose.

Genzken studied in Düsseldorf under Joseph Beuys, whose own art was influenced by Rudolf Steiner. Genzken's place, as a woman artist in Germany, and primarily a sculptor, has been difficult. Her best advocate, Benjamin HD Buchloh, says of Genzken: "To have to self-succumb to the totalitarian order of objects brings the sculptor to the brink of psychosis." This is something more than metaphor. Genzken's personal struggles are well-known within the art world. "That psychotic state," Buchloh concludes, "may well become the only position and practice the sculptor of the future can articulate."

Might something similar have been happening, too, for Af Klint? Genzken's work, like Af Klint's, is full of strange turns and diversions. Unlike Af Klint, she is not isolated, nor overshadowed by the extremes of Lutheran thought, or by the kinds of social repression at work in Swedish society a century ago. But life is just as difficult, and who is to say how the future will regard our own beliefs?

· Hilma af Klint and Isa Genzken are at the Camden Arts Centre, London NW3, until April 16. Details: 020-7472 5500; www.camdenartscentre.org